119 LearnersLast updated on May 26th, 2025
Factors of 3840
Factors are the numbers that divide any given number evenly without a remainder. In daily life, we use factors for tasks like sharing items equally, arranging things, etc. In this topic, we will learn about the factors of 3840, how they are used in real life, and tips to learn them quickly.
What are the Factors of 3840?
The numbers that divide 3840 evenly are known as factors of 3840.
A factor of 3840 is a number that divides the number without a remainder.
The factors of 3840 include 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 128, 160, 192, 240, 320, 384, 480, 640, 960, 1280, 1920, and 3840.
Negative factors of 3840: -1, -2, -3, -4, -5, -6, -8, -10, -12, -15, -16, -20, -24, -30, -32, -40, -48, -60, -64, -80, -96, -120, -128, -160, -192, -240, -320, -384, -480, -640, -960, -1280, -1920, and -3840.
Prime factors of 3840: 2, 3, and 5.
Prime factorization of 3840: 27 × 3 × 5.
The sum of factors of 3840: 1 + 2 + 3 + 4 + 5 + 6 + 8 + 10 + 12 + 15 + 16 + 20 + 24 + 30 + 32 + 40 + 48 + 60 + 64 + 80 + 96 + 120 + 128 + 160 + 192 + 240 + 320 + 384 + 480 + 640 + 960 + 1280 + 1920 + 3840 = 10896
How to Find Factors of 3840?
Factors can be found using different methods. Mentioned below are some commonly used methods:
- Finding factors using multiplication
- Finding factors using the division method
- Prime factors and prime factorization
Finding Factors Using Multiplication
To find factors using multiplication, we need to identify the pairs of numbers that are multiplied to give 3840. Identifying the numbers which are multiplied to get the number 3840 is the multiplication method.
Step 1: Multiply 3840 by 1, 3840 × 1 = 3840.
Step 2: Check for other numbers that give 3840 after multiplying
2 × 1920 = 3840
3 × 1280 = 3840
4 × 960 = 3840
5 × 768 = 3840
6 × 640 = 3840
8 × 480 = 3840
10 × 384 = 3840
12 × 320 = 3840
15 × 256 = 3840
16 × 240 = 3840
20 × 192 = 3840
24 × 160 = 3840
30 × 128 = 3840
32 × 120 = 3840
40 × 96 = 3840
48 × 80 = 3840
60 × 64 = 3840
Therefore, the positive factor pairs of 3840 are: (1, 3840), (2, 1920), (3, 1280), (4, 960), (5, 768), (6, 640), (8, 480), (10, 384), (12, 320), (15, 256), (16, 240), (20, 192), (24, 160), (30, 128), (32, 120), (40, 96), (48, 80), (60, 64). For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given numbers with whole numbers until the remainder becomes zero and listing out the numbers which result as whole numbers as factors. Factors can be calculated by following a simple division method -
Step 1: Divide 3840 by 1, 3840 ÷ 1 = 3840.
Step 2: Continue dividing 3840 by the numbers until the remainder becomes 0.
3840 ÷ 1 = 3840
3840 ÷ 2 = 1920
3840 ÷ 3 = 1280
3840 ÷ 4 = 960
3840 ÷ 5 = 768
3840 ÷ 6 = 640
3840 ÷ 8 = 480
3840 ÷ 10 = 384
3840 ÷ 12 = 320
3840 ÷ 15 = 256
3840 ÷ 16 = 240
3840 ÷ 20 = 192
3840 ÷ 24 = 160
3840 ÷ 30 = 128
3840 ÷ 32 = 120
3840 ÷ 40 = 96
3840 ÷ 48 = 80
3840 ÷ 60 = 64
Therefore, the factors of 3840 are: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 128, 160, 192, 240, 320, 384, 480, 640, 960, 1280, 1920, 3840.
Prime Factors and Prime Factorization
The factors can be found by dividing it with prime numbers. We can find the prime factors using the following methods:
- Using prime factorization
- Using factor tree
Using Prime Factorization: In this process, prime factors of 3840 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
3840 ÷ 2 = 1920
1920 ÷ 2 = 960
960 ÷ 2 = 480
480 ÷ 2 = 240
240 ÷ 2 = 120
120 ÷ 2 = 60
60 ÷ 2 = 30
30 ÷ 3 = 10
10 ÷ 5 = 2
2 ÷ 2 = 1
The prime factors of 3840 are 2, 3, and 5.
The prime factorization of 3840 is: 2^7 × 3 × 5.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 3840 is divided by 2 to get 1920.
Step 2: Now divide 1920 by 2 to get 960.
Step 3: Then divide 960 by 2 to get 480.
Step 4: Divide 480 by 2 to get 240.
Step 5: Divide 240 by 2 to get 120.
Step 6: Divide 120 by 2 to get 60.
Step 7: Divide 60 by 2 to get 30.
Step 8: Divide 30 by 3 to get 10.
Step 9: Divide 10 by 5 to get 2. Here, 2 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 3840 is: 27 × 3 × 5.
Factor Pairs: Two numbers that are multiplied to give a specific number are called factor pairs. Both positive and negative factors constitute factor pairs.
Positive factor pairs of 3840: (1, 3840), (2, 1920), (3, 1280), (4, 960), (5, 768), (6, 640), (8, 480), (10, 384), (12, 320), (15, 256), (16, 240), (20, 192), (24, 160), (30, 128), (32, 120), (40, 96), (48, 80), (60, 64).
Negative factor pairs of 3840: (-1, -3840), (-2, -1920), (-3, -1280), (-4, -960), (-5, -768), (-6, -640), (-8, -480), (-10, -384), (-12, -320), (-15, -256), (-16, -240), (-20, -192), (-24, -160), (-30, -128), (-32, -120), (-40, -96), (-48, -80), (-60, -64).
Common Mistakes and How to Avoid Them in Factors of 3840
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.
Mistake 1
Forgetting the number itself and 1 is a factor
Children might forget to add the given number itself and 1 as a factor. The number itself and 1 are the factors for every number. Always remember to include 1 and the number itself.
For example, in factors of 3840, 1 and 3840 are also factors.
Mistake 2
Missing Negative Factors
We have used only to mention positive factors every time. There are also negative factors, always check whether you have mentioned negative factors.
For example, The factors of 3840 consist of -1, -2, -3, etc.
Mistake 3
Including the Fraction
Children might sometimes consider fractions as factors. Only whole numbers can be factors.
For example, thinking 1.5 as a factor, because 3840/1.5 = 2560, and it is not a whole number.
Mistake 4
Confusing Factors With Prime Numbers
Remember that factors can be any whole numbers, not only just primes.
For example, thinking all the factors of 3840 are prime numbers.
For example, 2, 3, and 5 are the prime factors of 3840, but it has other factors like 4, 10, etc.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 3840 as 2^7 × 3 × 5 and missing all the key factors.
Factors of 3840 Examples
Problem 1
There are 3840 apples to be packed into boxes of 64 apples each. How many boxes are needed?
60 boxes are needed.
Explanation
To determine the number of boxes, divide the total apples by the number of apples per box. 3840/64 = 60
Problem 2
A rectangular field has an area of 3840 square meters and a width of 80 meters. Find the length.
48 meters.
Explanation
To find the length of the field, use the formula,
Area = length × width
3840 = length × 80
To find the value of length, divide 3840 by 80.
3840/80 = length
Length = 48.
Problem 3
There are 120 workers and 3840 tasks. How many tasks will each worker complete if they are distributed evenly?
Each worker will complete 32 tasks.
Explanation
To find the tasks each worker will complete, divide the total tasks by the number of workers.
3840/120 = 32
Problem 4
A warehouse has 3840 pallets, and they need to be stored in 240 sections. How many pallets will be in each section?
16 pallets in each section.
Explanation
Divide the total number of pallets by the number of sections to find how many pallets go into each section.
3840/240 = 16
Problem 5
A company produces 3840 units of a product. If they are packed into boxes containing 48 units each, how many boxes are required?
80 boxes are required.
Explanation
Divide the total units by the number of units per box.
3840/48 = 80
FAQs on Factors of 3840
1.What are the factors of 3840?
2.Mention the prime factors of 3840.
3.Is 3840 a multiple of 8?
4.Mention the factor pairs of 3840?
5.What is the square of 3840?
6.How can children in United States use numbers in everyday life to understand Factors of 3840?
7.What are some fun ways kids in United States can practice Factors of 3840 with numbers?
8.What role do numbers and Factors of 3840 play in helping children in United States develop problem-solving skills?
9.How can families in United States create number-rich environments to improve Factors of 3840 skills?
Important Glossaries for Factors of 3840
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 3840 include 1, 2, 3, 4, and others.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 5 are prime factors of 3840.
- Factor pairs: Two numbers in a pair that are multiplied to give the original number are called factor pairs. For example, the factor pairs of 3840 include (1, 3840), (2, 1920), etc.
- Prime factorization: The expression of a number as a product of its prime factors. For example, the prime factorization of 3840 is 2^7 × 3 × 5.
- Multiplication method: A method to find factors by identifying pairs of numbers that multiply to give the original number. For example, using this method for 3840, we find (1, 3840), (2, 1920), etc.
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Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
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